Rice, John Rischard (1959) The characterization of best nonlinear Tchebycheff approximations. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-02102006-083607
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Consider a continuous function, F([...]) of n parameters and [...]. Such a function is said to have Property NS if the following theorem is valid for every continuous function, f(x):
THEOREM: F([...]) is a best approximation to f(x) if and only if there are n+1 distinct points, [...], such that [...].
Depending an the basic assumptions on F, several sets of necessary and sufficient conditions are given for F to have Property NS. These conditions involve unisolvence and related concepts. The definition of Property NS is generalized and necessary and sufficient conditions on F are given for F to have this generalized property. The latter theory includes most common nonlinear approximating functions.
|Item Type:||Thesis (Dissertation (Ph.D.))|
|Degree Grantor:||California Institute of Technology|
|Division:||Physics, Mathematics and Astronomy|
|Thesis Availability:||Public (worldwide access)|
|Defense Date:||1 January 1959|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Imported from ETD-db|
|Deposited On:||10 Feb 2006|
|Last Modified:||26 Dec 2012 02:30|
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